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Finding the Third Proportional to 397 and 459

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Solution

The third proportional to 397 and 459 is: 530.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    397 : 459 = 459 : x
  2. Step 2: Convert to fraction form
    397/459 = 459/x
  3. Step 3: Cross multiply
    397x = 459 × 459
  4. Step 4: Simplify right side
    397x = 210,681
  5. Step 5: Solve for x
    x = 210,681/397
  6. Step 6: Final answer
    x = 530.68

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Why These Related Problems?

These problems maintain the same ratio (1.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.